d/(dt)(sin(t)+tcos(t))

解答

\frac{d}{d t} (sin (t) + t cos (t))

2 cos (t) - t sin (t)

求解步骤

\frac{d}{d t} (sin (t) + t cos (t))

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (sin (t)) + \frac{d}{d t} (t cos (t))

\frac{d}{d t} (sin (t)) = cos (t)

\frac{d}{d t} (t cos (t)) = cos (t) - t sin (t)

= cos (t) + cos (t) - t sin (t)

化简

= 2 cos (t) - t sin (t)

\frac{d}{d x} (ln ((6 x + 4) (3 x^{2} + 2)))

\int ln (11 x) d x

\int_{- 2}^{- 1} x^{2} e^{x^{3} + 8} d x

\frac{d}{d x} (- x^{π})

\int \frac{x + 3}{1 - x ^{2}} d x